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A quadrantal spherical triangle together with Napier's circle for use in his mnemonics. A quadrantal spherical triangle is defined to be a spherical triangle in which one of the sides subtends an angle of π /2 radians at the centre of the sphere: on the unit sphere the side has length π /2.
A quadrantal spherical triangle together with Napier's circle for use in his mnemonics. A quadrantal spherical triangle is defined to be a spherical triangle in which one of the sides subtends an angle of π /2 radians at the centre of the sphere: on the unit sphere the side has length π /2.
In a small triangle on the face of the earth, the sum of the angles is only slightly more than 180 degrees. A sphere with a spherical triangle on it. Spherical geometry or spherics (from Ancient Greek σφαιρικά) is the geometry of the two-dimensional surface of a sphere [a] or the n-dimensional surface of higher dimensional spheres.
Because these are double angles, each of q, r, and s represents two applications of the rotation implied by an edge of the spherical triangle. From the definitions, it follows that srq = uw −1 wv −1 vu −1 = 1, which tells us that the composition of these rotations is the identity transformation. In particular, rq = s −1 gives us
An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.
The elements of a polytope can be considered according to either their own dimensionality or how many dimensions "down" they are from the body.
Triangles have many types based on the length of the sides and the angles. A triangle whose sides are all the same length is an equilateral triangle, [3] a triangle with two sides having the same length is an isosceles triangle, [4] [a] and a triangle with three different-length sides is a scalene triangle. [7]
Spherical triangle. In spherical trigonometry, the half side formula relates the angles and lengths of the sides of spherical triangles, which are triangles drawn on the surface of a sphere and so have curved sides and do not obey the formulas for plane triangles. [1]